Bi-maximal Lepton Flavor Mixing Matrix and Neutrino Oscillation

Recently, many authors showed that if the solar and atmospheric neutrino data are both described by maximal mixing vacuum oscillations at the relevant mass scale, then there exists a unique bi-maximal lepton mixing matrix for three neutrino flavors. We construct the lepton mass matrices from the symmetry principle so that maximal mixings for the atmospheric and the solar neutrino vacuum oscillations are naturally generated. Although the hierarchical patterns of the lepton sector are quite different from each other, we show how two different mass matrices suggested in this work can be generated in a unified way. We also give comments on possible future tests of the bi-maximal lepton mixing matrix. PACS number(s): 14.60Pq, 12.15Fk [email protected], [email protected] [email protected], http://phya.yonsei.ac.kr/ ̃cskim/ 1 The recent atmospheric neutrino data from the Super-Kamiokande Collaboration [1] presents convincing evidence for neutrino oscillation and hence nonzero neutrino mass. The results indicate the maximal mixing between νμ and ντ with mass squared difference δm 2 atm ≃ 5×10−3 eV. The long-standing solar neutrino deficit [2, 3, 4] can also be explained through the matter enhanced neutrino oscillation (i.e. the MSW solution [5]) if δm2solar ≃ 6×10−6 eV and sin 2θsolar ≃ 7×10−3 (small angle case), or δm2solar ≃ 9×10−6 eV and sin 2θsolar ≃ 0.6 (large angle case) and through the long-distance vacuum neutrino oscillation called as “justso” oscillation [6] if δm2solar ≃ 10−10 eV and sin 2θsolar ≃ 1.0. However, the recent data on the electron neutrino spectrum reported by Super-Kamiokande [3] seems to favor the ”justso” vacuum oscillation, even though the small angle MSW oscillation and the maximal mixing between the atmospheric νμ and ντ have been taken as a natural solution for the neutrino problems [7]. Moreover, as shown by Georgi and Glashow [8], solar neutrino oscillations may be nearly maximal if relic neutrinos comprise at least one percent of the critical mass density of the universe. If this vacuum oscillation of the solar neutrino is confirmed in future experiments [3, 9], the mixing angles in the lepton sector are turned out to be large in contrast with the quark sector in which all observed mixing angles among different families are quite small. This seems not to be achieved in such a way to unify quarks and leptons at the GUT scale. One can thus deduce that the origin of the lepton mass matrices would be different from the one of the quark sector [7]. Therefore, it is worthwhile to find any possible mechanism providing such neutrino mixing patterns. Gauge models such as SO(10) grand unification model [10] and left-right symmetric model [11] have been constructed so that the so called “bi-maximal” neutrino mixing [12] for the solar and atmospheric vacuum oscillations are naturally accommodated. There have also been attempts to derive such a neutrino mixing from a lepton mass matrix ansatz [8, 12, 13]. Recently, Barger et al. [12] showed that if the solar and atmospheric neutrino data are both described by maximal mixing vacuum oscillations at the relevant mass scale, then there exists a unique mixing matrix for three neutrino flavors. Their solution necessarily conserves CP and automatically implies that there is no disappearance of atmospheric νe, consistent with indications from the Super-Kamiokande experiment. However, they did not construct the neutrino mass matrix from some simple symmetry principle, but inverted the process to obtain the neutrino mass matrix in the flavor basis from the mass eigenvalues and the bi-maximal mixing matrix by using the fact that a Majorana mass matrix or a hermitian Dirac mass matrix can be diagonalized by a single unitary matrix. From the phenomenological point of view, Georgi and Glashow [8] also suggested the neutrino mass